It depends upon the lay-out of the house. There are things you can do to facilitate air circulation. Cold air is heavier than warm air. The airs path will be the staircase as is. You could go to the corners of the rooms and cut holes to the first floor ceiling. That will increase the ability of the air to move and put it in the places you are trying to get cooled. Put them far from your staircase. Air is a fluid and it wants to move or more correctly can be induced to move. Think of your finger over a straw in a glass of water. With the finger on it you can lift the water out of the glass. Remove your finger and the water flows. I would try the passive idea first. If that doesn't work for you try the Tjernlund Air shares. They make floor to floor units and are very good. I've used them on project I was involved in by the thousands for heating and cooling.